Divide √95 / 3√5 . Provide an exact answer. (1 point)
To divide √95 by 3√5, you can follow these steps:
First, express the division as a fraction:
√95 / 3√5
Next, simplify the radical in the numerator by factoring out perfect squares if possible. In this case, we can't simplify √95 further because 95 doesn't have any square factors (it is the product of the prime numbers 5 and 19).
Now, let's rationalize the denominator. To do this, we want to get rid of the square root in the denominator by multiplying the numerator and the denominator by a term that will eliminate the square root. In this case, since we have √5 in the denominator, we should multiply the numerator and the denominator by √5. This will give us:
(√95 / 3√5) * (√5 / √5)
Now, multiply the numerators and the denominators:
(√95 * √5) / (3√5 * √5)
√(95 * 5) / (3 * 5)
√(475) / 15
Since there are no square factors in 475 (it is the product of the prime numbers 5 and 19, and 5 is repeated twice), we can simplify this by factoring out the perfect square from the radical:
√(25 * 19) / 15
(√25 * √19) / 15
(5 * √19) / 15
Now, you can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 5:
(5/5) * (√19 / 15/5)
1 * √19 / 3
√19 / 3
So the simplified exact answer of dividing √95 by 3√5 is:
√19 / 3